Solution of extremely large integral-equation problems

We report the solution of extremely large integral-equation problems involving electromagnetic scattering from conducting bodies. By orchestrating diverse activities, such as the multilevel fast multipole algorithm, iterative methods, preconditioning techniques, and parallelization, we are able to solve scattering problems that are discretized with tens of millions of unknowns. Specifically, we report the solution of a closed geometry containing 42 million unknowns and an open geometry containing 20 million unknowns, which are the largest problems of their classes, to the best of our knowledge.


Solution of large-scale scattering problems with the multilevel fast multipole algorithm parallelized on distributed-memory architectures
Ergül, Özgür Salih (2007-11-09)
We present the solution of large-scale scattering problems involving three-dimensional closed conducting objects with arbitrary shapes. With an efficient parallelization of the multilevel fast multipole algorithm on relatively inexpensive computational platforms using distributed-memory architectures, we perform the iterative solution of integral-equation formulations that are discretized with tens of millions of unknowns. In addition to canonical problems, we also present the solution of real-life problems...
Solutions of electromagnetics problems involving hundreds of millions of unknowns with parallel multilevel fast multipole algorithmt
Ergül, Özgür Salih (2009-06-05)
We present the solution of extremely large electromagnetics problems formulated with surface integral equations (SIEs) and discretized with hundreds of millions of unknowns. Scattering and radiation problems involving three-dimensional closed metallic objects are formulated rigorously by using the combined-field integral equation (CFIE). Surfaces are discretized with small triangles, on which the Rao-Wilton-Glisson (RWG) functions are defined to expand the induced electric current and to test the boundary c...
Rigorous Solutions of Electromagnetic Problems Involving Hundreds of Millions of Unknowns
Ergül, Özgür Salih (2011-02-01)
Accurate simulations of real-life electromagnetic problems with integral equations require the solution of dense matrix equations involving millions of unknowns. Solutions of these extremely large problems cannot be easily achieved, even when using the most powerful computers with state-of-the-art technology. Hence, many electromagnetic problems in the literature have been solved by resorting to various approximation techniques, without controllable error. In this paper, we present full-wave solutions of sc...
Comparison of Integral-Equation Formulations for the Fast and Accurate Solution of Scattering Problems Involving Dielectric Objects with the Multilevel Fast Multipole Algorithm
Ergül, Özgür Salih (2009-01-01)
We consider fast and accurate solutions of scattering problems involving increasingly large dielectric objects formulated by surface integral equations. We compare various formulations when the objects are discretized with Rao-Wilton-Glisson functions, and the resulting matrix equations are solved iteratively by employing the multilevel fast multipole algorithm (MLFMA). For large problems, we show that a combined-field formulation, namely, the electric and magnetic current combined-field integral equation (...
Iterative solution of composite problems with the combined-field integral equation
Ergül, Özgür Salih (2006-09-15)
We consider the solution of electromagnetic problems related to microwave applications involving composite geometries with coexisting open and closed conductors. Combined-field integral equation is introduced on the closed parts of the geometry to improve the iterative solutions. It is demonstrated that the convergence rates are significantly increased compared to the conventional formulation with the electric-field integral equation.
Citation Formats
Ö. S. Ergül and L. Gürel, “Solution of extremely large integral-equation problems,” 2007, Accessed: 00, 2020. [Online]. Available: